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Longitudinal Spin at RHIC. Cameron McKinney. 29 th Winter Workshop on Nuclear Dynamics February 7, 2013. Introduction: Longitudinal Spin at RHIC. From the RHIC Spin white paper (2012 ):

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Longitudinal Spin at RHIC

Cameron McKinney

29th Winter Workshop on Nuclear Dynamics

February 7, 2013

Introduction: Longitudinal Spin at RHIC

From the RHIC Spin white paper (2012):

Helicityparton density functions (PDFs) carry vital information on the extent to which quarks and gluons with a given momentum fraction x have their spins aligned with the spin direction of a fast moving nucleon in a helicityeigenstate. The corresponding integrals over all x relate to one of the most fundamental, but not yet satisfactorily answered questions in hadronic physics: how is the spin of the proton distributed among its constituents?

Proton Momentum

Proton Spin




, where superscript +(-)

indicates parton spin aligned (anti-aligned) with proton spin

Cameron McKinney

Proton spin:

Introduction: Longitudinal Spin at RHIC

Where does the proton’s spin of ½ come from?


RHIC longitudinal spin aims: ΔG and sea quark contribution to ΔΣ

Cameron McKinney


  • ΔG at RHIC

    • Accessing ΔG with double longitudinal spin asymmetries, ALL

    • Measuring ALL at RHIC

    • ΔG from ALL: Global analysis (by DSSV) with RHIC data

      • Impact of recent results from PHENIX+STAR

      • Next steps

  • Sea quark polarization at RHIC: the W program

    • Physics motivation: sea-quark polarization from ALW

    • Recent ALW results from STAR and PHENIX

    • Contribution of current and future data to DSSV global analysis


Cameron McKinney

Probing Helicity Structure in Polarized pp Collisions

Factorization: can break down cross section into pQCD-calculable hard scattering and pQCD-incalculable PDFs and fragmentation functions

pp  hX

Double longitudinal spin asymmetry is sensitive to Δgand Δq


Cameron McKinney

Measuring ALL at RHIC

  • ALLis measured by determining difference in particle yields between ++ and +- crossings (with an additional factor to normalize luminosities for crossing types)

  • Bunch spinpatterns include ++,+-, -+, and -- crossings in each fill

  • N is the yield of the final state measured

    • e.g. jets, di-hadron or di-jet states

Cameron McKinney



Measuring ALL at RHIC: ALLfor Inclusive Jets at STAR

STAR Run 6 inclusive jet

Mid-rapidity, s=200 GeV

PRD 86, 032006 (2012)

Process Fraction

pT [GeV]

  • STAR inclusive jet measurements at mid-rapidity have most statistics where qg processes dominatesensitive to sign of Δg

Good discriminative power between calculations with different assumptions for G


Cameron McKinney

Measuring ALL at RHIC: ALLfor Inclusive 0at PHENIX

PHENIX Run5+6 √s = 200 GeV: PRL103, 012003

Process Fraction

  • PHENIX ALL for inclusive π0 covers a scaled-down pT range compared to STAR—π0’s carry a fraction of jet momentum

  • Smallest statistical uncertainty where process fraction for gg ≈ qgweaker constraint on negative Δg, better constraints on positive Δg


Cameron McKinney

ΔG from ALL: QCD Global Analysis

  • DSSV (de Florian, Sassot, Stratmann, Vogelsang): global NLO analysis including polarized data from inclusive DIS, SIDIS, and RHIC pp collisions

    • Phys.Rev.Lett.101:072001, 2008 and Phys.Rev.D80:034030,2009.

Inclusive DIS data: routinely used for PDF fits

Semi-inclusive DIS data: previously used only in DNS fit

flavor separation

First RHIC polarized pp data: first fit by DSSV

467 data points in total (10% from RHIC)

Cameron McKinney

ΔG from ALL: QCD Global Analysis

  • Methodology Overview:

    • Parameterize distributions for quarks and gluons

    • Impose additional physics-based constraints (e.g. )

    • Evolve distributions from the input scale to the various Q2 of experimental data

    • Find corresponding observables as a function of kinematic variable (pTfor pp, x for DIS)

    • Minimize of fit of calculated observables to data

Cameron McKinney

ΔG from ALL: QCD Global Analysis

  • Methodology Overview:

Parameterize distributions…

…calculate observables and fit to data

(STAR and PHENIX Run 5 + Run 6 data shown).

DSSV: Phys.Rev.Lett.101:072001, 2008

Cameron McKinney

ΔG from ALL: DSSV Results

Well-determined by DIS

Main constraints to sea quarks from SIDIS (and DIS for strange quark)

Best constraints for ΔG now provided by RHIC

de Florian, Sassot, Stratmann, Vogelsang


Cameron McKinney

ΔG from ALL: Run 9 ALL Measurements at RHIC

STAR preliminary

  • Substantially larger figure of merit (P4L) from Run 9 than in all previous runs combined.

Cameron McKinney

ΔG from ALL: DSSV with Run 9 Data

  • DSSV++ is a new, preliminary global analysis from the DSSV group that includes 2009 ALL measurements from PHENIX and STAR

  • First experimental evidence of non-zero gluon polarization in the RHIC range (0.05 < x< 0.2)!

Cameron McKinney

ΔG from ALL: DSSV with Run 9 Data

Cameron McKinney

ΔG at RHIC: Next Steps

  • Large uncertainty still remains in both the shape of Δg(x) and its integral, particularly for small x region not yet accessed by RHIC data

  • RHIC will continue to improve constraints through the following:

    • Reduced statistical and systematic uncertainties for all ALL channels

    • Better handle on measured x through correlation measurements

    • Access lower x region through forward measurements and

Cameron McKinney

ΔG at RHIC: Next Steps: Correlation Measurements

Measure two jets or jet tags to constrain event kinematics; provides data on shape of

STAR di-jet projections;

one jet at forward rapidity (1<<2) to push down x2

ALL for back-to-back ’s at mid-rapidity—more data needed!

Cameron McKinney

ΔG at RHIC: Next Steps: Low x with the MPC in PHENIX

Larger  smaller x2

MPC: 3.1<<3.9

Projections of cluster ALLwith Run 13 for 2009 DSSV best fitand Δg upper uncertainty band

First PHENIX forward measurement of ALL for merged EM clusters (~80% 0)

Cameron McKinney

ΔG at RHIC: Next Next Steps: Electron-Ion Collider

  • Proposed electron-ion collider could greatly enhance our knowledge of Δ𝑮 beyond current capabilities of RHIC

    • Polarization of both electron (~80%) and proton beam (70%)

    • Very high luminosity (~10 fb-1 used for projection below achievable in 1-2 months of running)

    • Broad coverage in Q2 and x allows precise determination of Δg(x) through scaling violation


-w proj. EIC data

(~10 fb-1)


Cameron McKinney

Sea Quark Polarization: W Program at RHIC

Previously constrained by SIDIS:

Large uncertainties from fragmentation functions and lack of data

  • Measurement of parity-violating W production at RHIC complements SIDIS data

    • Leptonic final stateno FF dependence

    • Large Q2 ~ MW2

    • W couples only to left-handed quarks and right-handed anti-quarksfixes quark helicity and flavor

Cameron McKinney

W Program at RHIC: Forward Upgrades

  • Selecting kinematic ranges allows sensitivity to specific quark/anti-quark helicities; upgrades allow lepton measurements at forward rapidity

Forward Gem Tracker

  • Central (barrel) region (We , ||<1)

    • First data from 2009: PRL106, 062002 (2011)

  • Forward (endcap) region (We , 1<||<2) :

    • Forward tracker upgrade, first data in 2012

  • Central Arms (We , ||<0.35)

    • First data from 2009: PRL106, 062001 (2011)

  • Forward Arms (W , 1.2<||<2.4) :

    • Trigger upgraded, first data from 2011

RPC-1 North and RPC-3 North


Cameron McKinney

W Program at RHIC: Forward Measurements of AL

  • First measurement of by PHENIX in 2011 (

(towards )

Cameron McKinney

W Program at RHIC: Forward Measurements of AL

  • STAR preliminary AL for Run 12 already has sizeable effect on DSSV fits

DSSV++ (includes STAR Run 12)



Cameron McKinney

W Program at RHIC: Next Steps

  • Run 13 goal: finish W program by reaching total

Projections including expected data in 2013

Cameron McKinney


  • The PHENIX and STAR collaborations are making important contributions to our understanding of the helicity structure of the nucleon

  • ALL measurements provide best constraints to ΔG for QCD analyses

    • For the first time we see evidence of a non-zero gluon polarization

    • Large dataset from Run 13 at of 510 GeVwill lead to precise measurement of at 0.05 < x < 0.2

    • ALL for correlations and at forward rapidity will reduce uncertainties in the shape and integral of Δg(x) while broadening the coverage in x down to ~10-3

  • W program at RHIC will lead to substantial improvement in the understanding of the sea quark polarization in the near term with the expected statistics from Run 13

    • The STAR AL from Run 12 has already provided DSSV with a stronger constraint on the sea quark polarization

Cameron McKinney


Cameron McKinney

Constraining x/probing low x

Fwd–Rapidity 3.1<|η| < 3.9, 500 GeV



Effect of higher COM energy


Cameron McKinney

Central region: W  e from Run9







PHENIX: PRL106, 062001 (2011)

STAR: PRL106, 062002 (2011)

P=0.39 L=8.6/12 pb-1 in PHENIX/STAR


Cameron McKinney

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